# Partial Derivatives

### Some articles on partial derivatives, partial derivative, derivatives, derivative:

Reassignment Method - Efficient Computation of Reassigned Times and Frequencies
... cannot be applied directly to the discrete short-time Fourier transform data, because partial derivatives cannot be computed directly on data that is discrete in time and frequency, and ... It is possible to approximate the partial derivatives using finite differences ... For example, the phase spectrum can be evaluated at two nearby times, and the partial derivative with respect to time be approximated as the difference between the two ...
Triple Product Rule
... cyclical rule or Euler's chain rule, is a formula which relates partial derivatives of three interdependent variables ... Here the subscripts indicate which variables are held constant when the partial derivative is taken ... That is, to explicitly compute the partial derivative of x with respect to y with z held constant, one would write x as a function of y and z and take the ...
ADMB - History and Background - Implementation
... partial derivatives of the likelihood with respect to all model variables) must also be done with the same accuracy as the likelihood computation itself ... Fournier developed a protocol for writing code to compute the required derivatives based on the chain rule of differential calculus ... code segments the objective function adjoint code to compute the partial derivatives of the objective function with respect to the parameters to be estimated dedicated ...
Holomorphic Function - Definition
... function ƒ of a single complex variable, the derivative of ƒ at a point z0 in its domain is defined by the limit This is the same as the definition of ... y) is holomorphic, then u and v have first partial derivatives with respect to x and y, and satisfy the Cauchy–Riemann equations or, equivalently, the Wirtinger derivative of ƒ with ... is that if u and v have continuous first partial derivatives and satisfy the Cauchy–Riemann equations, then ƒ is holomorphic ...
Generalizations Of The Derivative - Derivatives in Analysis - Higher-order Derivatives and Differential Operators
... One can iterate the differentiation process, that is, apply derivatives more than once, obtaining derivatives of second and higher order ... A more sophisticated idea is to combine several derivatives, possibly of different orders, in one algebraic expression, a differential operator ... we consider a particular linear combination of zeroth, first and second order derivatives "all at once" ...

### Famous quotes containing the word partial:

The only coöperation which is commonly possible is exceedingly partial and superficial; and what little true coöperation there is, is as if it were not, being a harmony inaudible to men. If a man has faith, he will coöperate with equal faith everywhere; if he has not faith, he will continue to live like the rest of the world, whatever company he is joined to.
Henry David Thoreau (1817–1862)